 Hi and welcome to the session. I am Asha and I am going to help you with the following position which says, determine the domain and range of the relation R defined by all the ordered here x, x plus 5 such that x belong to the set 0, 1, 2, 3, 4, 5. First let us learn what is a relation. Suppose we have any two non-empty sets A and B. The relation from A to B is a subset of the Cartesian product of A and B which is defined by all those ordered where x and y such that x belong to A and y belong to B. Now the set of all the first element of these ordered pairs, the domain of the relation, the second element of the ordered pair is called the range of the relation and this relation is derived by describing a relationship between the first element and the second element of the ordered pair in A to B and the second element is called the image of the first element. So with the help of this definition it will solve the above problem so this is our key idea. Let us start with the solution given a relation defined by the set of all the ordered pair x for my x plus 5 such that x belong to the set having element 0, 1, 2, 3, 4 and 5 and x is equal to 0, 1, 2, 3, 4 and 5 then the value of x is 5 is equal to first when x is equal to 0 then x plus 5 is 5, x is 1, x plus 5 becomes 6 when x is 2 then x plus 5 becomes 7, when x is 3 then 3 plus 5 becomes 8 and when x is 4, 4 plus 5 becomes 9 and when x is 5 then 5 plus 5 becomes 10. Therefore the set R, all the ordered pairs when x is 0 then x plus 5 is 5 similarly then we have 1, 6, 2, 7, 4, 9 and 5, 10. The domain of R will be the set of all the first element of these ordered pairs and which are 0, 1, 2, 3, 4 and 5 and the range of R is the set of all the elements which are the second element of these ordered pairs, set 5, 6, 7, 8, 9 and 10. So our answers are first we have to find the domain of R, so domain of R is set having element 0, 1, 2, 3, 4 and 5 and range of R is the set having elements 5, 6, 7, 8, 9 and 10. So this completes the solution, hope you enjoyed it, take care and have a good day.